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Geometry of Quantum States: An Introduction to Quantum Entanglement
Abstract
Quantum information theory is at the frontiers of physics, mathematics and information science, offering a variety of solutions that are impossible using classical theory. This book provides an introduction to the key concepts used in processing quantum information and reveals that quantum mechanics is a generalisation of classical probability theory. After a gentle introduction to the necessary mathematics the authors describe the geometry of quantum state spaces. Focusing on finite dimensional Hilbert spaces, they discuss the statistical distance measures and entropies used in quantum theory. The final part of the book is devoted to quantum entanglement - a non-intuitive phenomenon discovered by Schrödinger, which has become a key resource for quantum computation. This richly-illustrated book is useful to a broad audience of graduates and researchers interested in quantum information theory. Exercises follow each chapter, with hints and answers supplied.
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“An important theorem in classical polarization optics states that any linear optical element ͑either deterministic or stochastic͒ is equivalent to a composite device made of at most four nondepolarizing elements in parallel ͓32͔.”
From Linear optics and quantum maps (2007) · cites this paper as [32]
In the citing paper
“A result that may be useful in this direction of research is the 'concentration of measure effect' of the gate fidelity which implies that as n increases, the measure of the set of states which produce a fidelity close to the minimum yet far from the average is exponentially small in n [41, 42].”
From Characterizing quantum gates via randomized benchmarking (2012) · cites this paper as [42]
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“…they have not escaped the attention of mathematical physicists and applied mathematicians (Byrd and Khaneja, 2003; Kimura and Kos- Published by Copernicus Publications on behalf of the Groupement AMPERE. sakowski, 2005; Bengtsson and Zyczkowski, 2006; Goyal et al., 2016; Szymański et al., 2018).”
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Metadata
- Authors
- Bengtsson, I., & Zyczkowski, K.
- Affiliations
- Stockholm University (SE)
- ORCID
- Bengtsson, Ingemar
- Venue
- Cambridge University Press eBooks
- Publisher
- Cambridge University Press
- Published
- 2006-05-11
- OpenAlex
- W360650912
- Cited by
- 1,357
- References
- 0
- Citations by year
- 2026: 50 · 2025: 82 · 2024: 65 · 2023: 53 · 2022: 64 · 2021: 75 · 2020: 81 · 2019: 74 · 2018: 66 · 2017: 62 · 2016: 96 · 2015: 83 · 2014: 81 · 2013: 90 · 2012: 60
- FWCI
- 20.23
- Type
- book
- Language
- en
- Open access
- closed
- Locations
- Cambridge University Press eBooks (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Keywords
- quantum information, quantum state space, finite-dimensional Hilbert space, statistical distance measures, quantum entropy, quantum entanglement, quantum computing
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